Originally, during the Roman republic, the word maiestas was the legal term for the supreme status and dignity of the state, to be respected above everything else. [...] It was first assumed by Charles V, Holy Roman Emperor, who believed that, as an emperor,
he deserved a style greater than Highness, which had been used by preceding emperors and
kings. Soon, King Francis I of France and King Henry VIII of England followed his example.

What I take from all this is:

The word lord, originally and all throughout its history, referred to someone, a person (or a personification of God, as opposed to God as an abstract concept). It's only natural to refer to my guardian, my ruler and my master as, well, my guardian, ruler and master rather than your, his or her guardian, ruler and master.

The word majesty, on the other hand, always referred to something, a concept,
a trait that was attributed to someone — much like highness, honor, and excellence. When I am talking about a king (or a judge), I attribute majesty (or honor) to him rather than to myself.

Explaining "my lord" is easy, "my lord" is the person who is the lord of me. "Your lord" would be the person who is the lord of you rather than me.

The function of the possessive (your, her, his) in "your majesty" or "her majesty" or "his royal highness" seems to be to indicate that the noun indicates a person, but this is some kind of archaic or rare usage.

I completely agree with the sentiment, but completely disagree with the etymology. The adjective majestic was derived from the much older noun majesty around 1600, not the other way round.
–
RegDwigнt♦Sep 9 '10 at 18:36

Very succinctly, majesty, grace, honor, and royal highness are qualities of the exalted person being addressed, while lord, liege, and king are titles describing the superior relationship of the one addressed (superior to me, that is).

This is the best answer by far. Here's hoping it'll eventually get voted above the others...
–
MarthaªNov 16 '10 at 18:28

3

Yes. That is why in the High Court (and above) in England we address the judges as "my Lord" but refer to them as "your Lordship" - the second is a quality they possess rather than a reference to themselves. Example "My Lord, has your Lordship read the agreed trial bundle?"
–
Francis DaveyFeb 11 '14 at 9:32

A little late to this party, but it seems to me that no-one has made the most important point: namely that it's "my Lord", but "your Lordship" -- the point being that one refers to the individual directly ("my Lord"), and the other refers to the same individual obliquely ("your Lordship"), and is a kind of metonymy.